Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
0 - 9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
260 - 269
270 - 279
280 - 289
290 - 299
300 - 309
310 - 319
320 - 329
330 - 339
340 - 349
350 - 359
360 - 369
370 - 379
380 - 389
390 - 399
400 - 409
410 - 419
420 - 429
430 - 439
440 - 445
>
11
12
13
14
(2)
15
(3)
16
(4)
17
(5)
18
(6)
19
(7)
20
(8)
<
0 - 9
10 - 19
20 - 29
30 - 39
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
260 - 269
270 - 279
280 - 289
290 - 299
300 - 309
310 - 319
320 - 329
330 - 339
340 - 349
350 - 359
360 - 369
370 - 379
380 - 389
390 - 399
400 - 409
410 - 419
420 - 429
430 - 439
440 - 445
>
page
|<
<
(29)
of 445
>
>|
<
echo
version
="
1.0
">
<
text
type
="
book
"
xml:lang
="
la
">
<
div
xml:id
="
echoid-div7
"
type
="
body
"
level
="
1
"
n
="
1
">
<
div
xml:id
="
echoid-div7
"
type
="
chapter
"
level
="
2
"
n
="
1
">
<
div
xml:id
="
echoid-div94
"
type
="
math:theorem
"
level
="
3
"
n
="
44
">
<
p
>
<
s
xml:id
="
echoid-s389
"
xml:space
="
preserve
">
<
pb
o
="
29
"
rhead
="
THEOR. ARITH.
"
n
="
41
"
file
="
0041
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0041
"/>
to maiore
<
var
>.c.t.</
var
>
extractum quare reſiduum qua-
<
lb
/>
<
figure
xlink:label
="
fig-0041-01
"
xlink:href
="
fig-0041-01a
"
number
="
56
">
<
image
file
="
0041-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0041-01
"/>
</
figure
>
drati
<
var
>.c.p.</
var
>
cognitum erit, quam quantitatem co-
<
lb
/>
gnitam, cum ſit ſecundo loco data, cogitemus
<
lb
/>
detrahi è toto quadrato cognito
<
var
>.q.e.</
var
>
ex quo
<
lb
/>
ſumma duorum ſupplementorum
<
var
>.q.o.</
var
>
et
<
var
>.o.e.</
var
>
<
lb
/>
cognoſcetur, vnà cum quadratis
<
var
>.u.n.</
var
>
et
<
var
>.p.a.</
var
>
du
<
lb
/>
plo ſcilicet
<
var
>.q.a.</
var
>
quo diuiſo per duplum
<
var
>.q.h.</
var
>
aut
<
lb
/>
ſimplex
<
var
>.q.a.</
var
>
per
<
var
>.q.h.</
var
>
ſimplicem, dabitur
<
var
>.a.h.</
var
>
<
lb
/>
nempe
<
var
>.p.h.</
var
>
minor numerus quæſitus.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div96
"
type
="
math:theorem
"
level
="
3
"
n
="
45
">
<
head
xml:id
="
echoid-head61
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
45
">XLV</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s390
"
xml:space
="
preserve
">CVR volentes diuidere numerum propoſitum in duas eiuſmodi partes, vt pro
<
lb
/>
ductum vnius in alteram, alteri numero propoſito æquetur, rectè dimidium
<
lb
/>
primi dati numeri in ſeipſum multiplicant, ex quo quadrato ſecundum datum nu-
<
lb
/>
merum detrahunt,
<
reg
norm
="
reſiduique
"
type
="
simple
">reſiduiq́;</
reg
>
radicem ſumunt, qua coniuncta vni dimidio primi nu-
<
lb
/>
meri, pars maior datur, ex altero verò dimidio detracta, minorem manifeſtabit.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s391
"
xml:space
="
preserve
">Exempli gratia, ſi numerus partiendus eſſet .34. alter verò numerus eſſet .64. cui
<
lb
/>
productum vnius partis in alteram æquale eſſe deberet. </
s
>
<
s
xml:id
="
echoid-s392
"
xml:space
="
preserve
">Dimidium primi numeri, in
<
lb
/>
ſeipſum multiplicaremus, cuius quadratum eſſet .289. de quo detracto ſecundo nu-
<
lb
/>
mero nempe .64. remaneret .225. cuius quadrata radix nempe .15. coniuncta .17.
<
lb
/>
dimidio .34. proferet .32. maiorem partem,
<
reg
norm
="
detractoque
"
type
="
simple
">detractoq́;</
reg
>
ex .17. ſupereſſet .2. pars
<
lb
/>
inquam minor.</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s393
"
xml:space
="
preserve
">Cuius ſpeculationis cauſa, primus numerus propoſitus ſignificetur linea
<
var
>.a.d.</
var
>
cu-
<
lb
/>
ius dimidium
<
var
>.c.d.</
var
>
cognitum erit, vnà etiam eius quadratum
<
var
>.c.f.</
var
>
quo diuiſo per dia
<
lb
/>
metrum
<
var
>.e.d.</
var
>
ſupponantur partes ignotæ
<
lb
/>
<
figure
xlink:label
="
fig-0041-02
"
xlink:href
="
fig-0041-02a
"
number
="
57
">
<
image
file
="
0041-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0041-02
"/>
</
figure
>
ipſius
<
var
>.a.d.</
var
>
eſſe
<
var
>.a.b.</
var
>
et
<
var
>.b.d.</
var
>
& à puncto
<
var
>.b.</
var
>
<
lb
/>
duci lineam
<
var
>.b.h.g.</
var
>
parallelam
<
var
>.d.f.</
var
>
et
<
var
>.m.
<
lb
/>
h.k.</
var
>
parallelam
<
var
>.d.a.</
var
>
extructa figura ſimi
<
lb
/>
li figuræ quintæ ſecundi Eucli. </
s
>
<
s
xml:id
="
echoid-s394
"
xml:space
="
preserve
">quare da
<
lb
/>
bitur
<
reg
norm
="
gnomon
"
type
="
context
">gnomõ</
reg
>
<
var
>.l.d.g.</
var
>
æqualis producto
<
var
>.b.
<
lb
/>
k.</
var
>
& proinde cognitus, quo detracto è
<
lb
/>
quadrato,
<
var
>c.f.</
var
>
remanebit quadratum
<
var
>.g.l.</
var
>
<
lb
/>
cuius radice æquali
<
var
>.c.b.</
var
>
coniuncta
<
var
>.a.c.</
var
>
<
lb
/>
& detracta ex
<
var
>.c.d.</
var
>
partes
<
var
>.a.b.</
var
>
et
<
var
>.b.d.</
var
>
quæſitæ dabuntur.</
s
>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div98
"
type
="
math:theorem
"
level
="
3
"
n
="
46
">
<
head
xml:id
="
echoid-head62
"
xml:space
="
preserve
">THEOREMA
<
num
value
="
46
">XLVI</
num
>
.</
head
>
<
p
>
<
s
xml:id
="
echoid-s395
"
xml:space
="
preserve
">CVR propoſitis tribus numeris, quorum prior in duas eiuſmodi partes diui-
<
lb
/>
dendus ſit, ut mutuò diuiſæ, & per ſummam prouenientium diuiſo ſecundo
<
lb
/>
numero, proueniens vltimum ſit æquale tertio numerorum propoſitorum. </
s
>
<
s
xml:id
="
echoid-s396
"
xml:space
="
preserve
">Conſul
<
lb
/>
tiſsimum ſit ſecundum numerum per tertium diuidere, ex quo proueniens ſit ſum-
<
lb
/>
ma prouenientium è duabus partibus mutuò diuiſis, quam ſummam ſi quis velit di-
<
lb
/>
ſtinguere, rectè poſſit medio operationis
<
reg
norm
="
pręcedentis
"
type
="
context
">pręcedẽtis</
reg
>
theorematis
<
reg
norm
="
sumpta
"
type
="
context
">sũpta</
reg
>
vnitate ſuper
<
lb
/>
ficiali pro ſecundo numero diſtinctis poſtmodum prouenientibus, rectè meo iudi-
<
lb
/>
cio operabimur per
<
reg
norm
="
regulam
"
type
="
context
">regulã</
reg
>
de tribus (quod fuit ab antiquis prætermiſſum) Si dixe- </
s
>
</
p
>
</
div
>
</
div
>
</
div
>
</
text
>
</
echo
>